Abstract
AbstractIn this paper, by using a change of variable and the mountain-pass theorem, we show that the following quasilinear Schrödinger systems $$ \textstyle\begin{cases} -\triangle u+V_{1}(x)u+\frac{\kappa}{2}[\triangle \vert u \vert ^{2}]u=\lambda f(x,u, v), & x\in \mathbb{R}^{N}, \\ -\triangle v+V_{2}(x)v+\frac{\kappa}{2}[\triangle \vert v \vert ^{2}]v=\lambda h(x,u, v), & x\in \mathbb{R}^{N} \end{cases} $$
{
−
△
u
+
V
1
(
x
)
u
+
κ
2
[
△
|
u
|
2
]
u
=
λ
f
(
x
,
u
,
v
)
,
x
∈
R
N
,
−
△
v
+
V
2
(
x
)
v
+
κ
2
[
△
|
v
|
2
]
v
=
λ
h
(
x
,
u
,
v
)
,
x
∈
R
N
have a nontrivial solution $(u, v)$
(
u
,
v
)
for all $\lambda >\lambda _{1}(\kappa )$
λ
>
λ
1
(
κ
)
, where $N\geq 3, V_{1}(x), V_{2}(x)$
N
≥
3
,
V
1
(
x
)
,
V
2
(
x
)
are positive continuous functions, κ, λ are positive parameters, and nonlinear terms $f, h\in C(\mathbb{R}^{N}\times \mathbb{R}^{2}, \mathbb{R})$
f
,
h
∈
C
(
R
N
×
R
2
,
R
)
. Our main contribution is that we can deal with the case when $\kappa >0$
κ
>
0
is large for the above systems.
Funder
National Natural Science Foundation of China
Yunnan Local Colleges Applied Basic Research Projects
Technology Innovation Team of University in Yunnan Province
Yunnan Fundamental Research Projects
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Cited by
1 articles.
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